Remark 2.17  If \(f\)  is a \(\mathbf {R}\) -valued convex
function on an open subset \(U\)  of \(X\)  then \(\nabla f(x)\)  is non empty for
every \(x \in U\) ; cf. [1]}. Moreover, \(f\)  is
differentiable of order 1 at \(x\)  if and only if \(\nabla f(x)\)  is a
singleton; cf. [1]}.

